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feat(ClassicalMechanics): add the Poisson bracket - #1698

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feat(ClassicalMechanics): add the Poisson bracket#1698
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Sudo-RR:classical-poisson-bracket

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@Sudo-RR Sudo-RR commented Sep 29, 2026

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  • poissonBracket, antisymmetry, bilinearity in each argument, and deriv_comp_eq_poissonBracket connecting it to time evolution under Hamilton's equations.
  • gradient_add in Physlib.Mathematics.Calculus.Gradient, the missing additivity rule needed to prove bilinearity.

@Sudo-RR @claude
feat(ClassicalMechanics): add the Poisson bracket
16f74e6 
- `poissonBracket`, antisymmetry, bilinearity in each argument, and
  `deriv_comp_eq_poissonBracket` connecting it to time evolution under
  Hamilton's equations.
- `gradient_add` in `Physlib.Mathematics.Calculus.Gradient`, the missing
  additivity rule needed to prove bilinearity.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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@Sudo-RR Sudo-RR changed the title feat(ClassicalMechanics): add the Poisson bracket feat(ClassicalMechanics): add the Poisson bracket -t classical mechanics Sep 29, 2026
@Sudo-RR Sudo-RR changed the title feat(ClassicalMechanics): add the Poisson bracket -t classical mechanics feat(ClassicalMechanics): add the Poisson bracket Sep 29, 2026
@Sudo-RR @claude
docs(ClassicalMechanics): list poissonBracket_add_right and poissonBr…
10db15f 
…acket_const_mul_right

- The key results of `PoissonBracket.lean` list the right-argument
  bilinearity lemmas `poissonBracket_add_right` and
  `poissonBracket_const_mul_right`, which the file states, instead of
  saying that they follow by antisymmetry.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
jstoobysmith
jstoobysmith reviewed Sep 30, 2026
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A couple of small comments from me here.

Comment thread Physlib/ClassicalMechanics/PoissonBracket.lean

/-- The time derivative of a phase-space function `f` composed with trajectories `p q : Time → X`
is the sum of the gradients of `f` paired with the velocities `∂ₜ p` and `∂ₜ q`. -/
theorem deriv_comp_eq_inner_gradient_add (f : X → X → ℝ) (p q : Time → X) (t : Time)

@jstoobysmith jstoobysmith Sep 30, 2026

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This should likely be a lemma I think

Comment thread Physlib/ClassicalMechanics/PoissonBracket.lean

@jstoobysmith jstoobysmith Sep 30, 2026

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I think we should put this and Physlib.ClassicalMechanics.HamiltonsEquations in a new subdirectory called ./HamiltonianMechanics

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jstoobysmith commented Sep 30, 2026

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